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solutionset10 - Problem Set 10 Solutions STAT 3022 section...

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Unformatted text preview: Problem Set 10 Solutions STAT 3022, section 001 11/29/2011 13.12. First Serial Correlation Coefficient. The pooled estimate for c is (34)(201 . 45) + (37)(183 . 08) + (32)(162 . 96) + (40)(190 . 53) 34 + 37 + 32 + 40 = 185 . 03 , the pooled estimate for c 1 is (34)(49 . 83) + (37)(106 . 37) + (32)(85 . 49) + (40)(78 . 83) 34 + 37 + 32 + 40 = 80 . 55 , and the pooled estimate for r 1 is 80 . 55 185 . 03 = . 4353 18.9. Heart Disease and Obesity in American Samoan Men. CVD death Yes No Totals Obese 22 1,179 1,201 Not obese 22 1,409 1,431 (a) Wish to estimate π 1- π 2 : (i) The sample proportions of CVD deaths for the obese (group 1) and nonobese (group 2) groups are: ˆ π 1 = 22 1201 = . 01832 and ˆ π 2 = 22 1431 = . 01537 (ii) The standard error for ˆ π 1- ˆ π 2 (C.I. version) is SE(ˆ π 1- ˆ π 2 ) = s ˆ π 1 (1- ˆ π 1 ) n 1 + ˆ π 2 (1- ˆ π 2 ) n 2 = r ( . 01832)( . 98168) 1201 + ( . 01537)( . 98463) 1431 = 0.00505 (iii) A 95% confidence interval for π 1- π 2 is ˆ π 1- ˆ π 2 ± z ( . 975)SE(ˆ π 1- ˆ π 2 ) = (0 . 01832- . 01537) ± (1 . 96)(0 . 00505) =- . 00696 to . 01285 . (b) Wish to test H : π 1- π 2 = 0 vs. H a : π 1- π 2 > 0. The z-statistic is z = ˆ π 1- ˆ π 2 SE(ˆ π 1- ˆ π 2 ) = . 00295 . 00505 = 0 . 5825 The one-sided p-value is P ( Z > . 5825) = . 2801 (c) Wish to estimate ω 1 /ω 2 : (i) The sample odds of CVD death for the obese and nonobese groups are ˆ ω 1 = 22 1179 = . 01866 and ˆ ω 2 = 22 1409 = . 01561 (ii) The estimated odds ratio is ˆ φ = ˆ ω 1 / ˆ ω 2 = 1 . 195 (iii) The standard error of the estimated log odds ratio is SE(log(ˆ ω 1 / ˆ ω 2 )) = r 1 22 + 1 1179 + 1 22 +...
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solutionset10 - Problem Set 10 Solutions STAT 3022 section...

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